What is Qubit: Definition and 80 Discussions

In quantum computing, a qubit () or quantum bit (sometimes qbit) is the basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.

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  1. V

    Mathematica Calculating Concurrence in Mathematica: Solving 2-Qubit States | Tutorial

    Hi guys! I have an unsolved problem. I'm going to calculate the concurrence for pure 2-qubit states: |Ψ>=a| up up >+b|up down> +c|down up> +d | down down > where up and down stay for uparrow and downarrow. The concurrence is defined as: C = 2|ad-bc|≥0 I have found the vector Ψ3= 1/2 (1,1, cos...
  2. ant0n

    How would observation of the state of qubits affect them?

    Firstly, I apologise for any lack of understanding, incorrect assumptions or misinterpretations of the very little I know about physics, quantum mechanics & quantum computing. I am not an academic, scientist or mathematician, but a software engineer with an interest in quantum computing and...
  3. nomadreid

    What is the correct interpretation of a qubit with v= 0.6|0> + 0.8|1>?

    This is undoubtedly one of the more basic (not to say stupid) questions ever to appear in this rubric. But here goes: Suppose you have v= 0.6|0> + 0.8|1>. This means that there is 36% chance of measuring |0> and 64% chance of measuring |1>. Otherwise put, given a million particles in this...
  4. nomadreid

    To measure only one qubit of two

    If you have a two-qubit system |x>[(|0>-|1>)/√2], whereby x∈{0,1}, and you want to just know x, do you (a) assume that this means that |x> belongs to one particle, (|0>-|1>)/√2 to another particle, so you just measure the first particle? or (b) if you can't tell the particles apart, pass this...
  5. J

    Measuring a Qubit: Understanding Pauli Matrices

    I undertand that measuring a qubit's spin along a particular axis yields one of the eigenstates of the corresponding pauli matrices. I'm a little confused about what this type of measurement looks like mathematically. i.e how do you show the actual act of observing the qubits spin using the...
  6. M

    General 3-Qubit Mixed State: 63 Variables & Bloch Vectors

    How do I write the general form of a 3 qubit mixed state ? It has 63 variables. Well one way is to use bloch vectors. So basically we take 3 single qubit mixed states (3 variables each) and tensor product them. Then we add the 2 qubit correlators and 3 qubit correlator terms. Finally we can...
  7. Elroy

    Qubit Math: Partitioning Phi into BetaA and BetaB

    Hi All, I'm gradually teaching myself quantum computing, being an excellent programmer and fair at linear algebra and geometry. To learn it, I'm writing a quantum computer emulator (complete with graphical representations). I'll share it when I get to some level of completion. The following...
  8. A

    Qubits Entanglement: Calculate & Interpret

    Homework Statement Determine which qubits are entangled: ##|\psi\rangle=\frac{1}{2}(|000\rangle+i|010\rangle+i|101\rangle-|111\rangle)## Homework EquationsThe Attempt at a Solution [/B] My idea was to first calculate the density operator ##\rho = |\psi\rangle \langle\psi|## and then find...
  9. J

    Can a two-qubit state be proven to be non-entangled using contraposition?

    Hi I'm going through some course notes for QM. A state for a 2 qubit system is called non-entangled (or separable) if it can be decomposed in a tensorproduct of 2 single qubit states. If we write a general state as |\psi> = a_{00}|00>+a_{01}|01>+a_{10}|10>+a_{11}|11> A theorem states...
  10. Thinkor

    Can information truly be teleported using quantum entanglement?

    I have seen numerous articles referencing the teleportation of information over a distance of 3 meters using quantum entanglement. I don't believe it. That would contradict special relativity, would it not? You could, for example, decide which of two observers moving relatively to one...
  11. L

    Qubit system, time dependent states.

    Homework Statement See attachment Homework Equations The Attempt at a Solution (i) |\Psi(t)_{1}>=e^{{-itE_{1}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>+|z^{-}>) |\Psi(t)_{2}>=e^{{-itE_{2}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>-|z^{-}>) where...
  12. V

    Current standing of qubit research

    Good day everyone, I apologize if this is not the correct forum; in some way it is a homework question but not of the ordinary form. This semester I will be writing a ~3000 word paper on the topic of the current standing in qubit research, where I will be describing and comparing various...
  13. S

    A question about Qubit (number of states)

    Hi I read this information about the Qubit: "N Qubits are equivalent 2^N classical bits (2^N states)" But I couldn't understand that, because I know that each single Qubit could be one and zero at the same time, so each single Qubit is equivalent two classical bits (two states) That...
  14. N

    How to find existence of quantum discord in two qubit state

    Homework Statement Hello, I have a following problem. For a three-qubit state i need to trace subsystem. For this subsystem AB I calculate eigenvalues and eigenvectors. The task is now to determine according the eigenvalues and eigenvectors whether quantum discord in this system is non-zero...
  15. R

    Bra-ket notation and qubit issue.

    I am having trouble understanding the following: Uf: |x>|y> → |x>|y \oplusf(x)> \oplus being a mod 2 operation (nand)? I suppose I don't understand how to read the "ket" states so well. As far as I understand we have that since x and y can be 0,1 only if |x=1>|y=1> then if f(x) = 1 then...
  16. S

    Forming the most general two qubit entangled state & parametrizing it.

    I have seen four two qubit entangled states of the form: $ \frac{1}{\sqrt{2}} \left | 00 \right > \pm \left | 11 \right >$ $ \frac{1}{\sqrt{2}} \left | 01 \right > \pm \left | 10 \right >$ I want to write a most general two qubit entangled state. I presume it can be of the form: $...
  17. R

    Two qubit state multiplication

    Hi guys having a little trouble with two-qubit state multiplication. Could you tell me how you work out the following? (not only the answers but the working out) I need to be able to understand these calculations before I can move on to the next step of an entanglement question. I understand...
  18. L

    Qubit Spin Convention: |0> & |1> Eigenvectors?

    This is a bit embarrassing, but by convention does |0> = (1,0)^T and |1>=(0,1)^T, where we are in the basis of the eigenvectors of \sigma_{z}?
  19. R

    Constructing a Toffoli gate with qubit gates?

    I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how to do this, or how to verify it (fig 4.8 in his book) I've attached a photo of the diagram...
  20. S

    Measuring a qubit in a different basis

    Hi, I'm a student of computer science and am writing a simulator for Measurement-based quantum computing or one-way quantum computing (it's based on the paper "The Measurement Calculus" by Elham Kashefi et al.). Anyway, I'm still a bit confused when it comes to the calculations. If we write...
  21. J

    Many questions about qubit (quantum computing)

    Hello! I am new here and I will try my best to clarify my questions and not violate the forum rules. Just for the record, I am not particularly good at understanding equation-saturated explanations because I am not an expert. However, I did a lot of searching and I still don't understand...
  22. R

    One qubit modeling the universe

    I just had a weird thought. One qubit is a 2-d complex vector space which is isomorphic to a 4-d real vector space. Why can't we model the 4-manifold of space-time universe using one qubit?
  23. R

    What is the most scalable qubit candidate for quantum computing?

    Whats most scalable qubit candidate so far ? - - Thanks, Vvk
  24. M

    Preparation of Single qubit mixed states

    Hi, I would like to ask some questions in regards to preparing mixed states. Assuming I am allowed to prepary any pure quantum state, perform measurements and apply unitaries, I am asked to prepare a single qubit quantum state of maximum entropy. As I understand, a 1-qubit quantum...
  25. Y

    Quantum optics, 2 qubit gates acting on 2 qubits - cannot be factorized?

    Quantum optics, 2 qubit gates acting on 2 qubits - cannot be factorized?? Hi, I'm struggling to understand why two qubit gates acting on two qubits cannot be factorized, i.e. G12 \neq G1 \otimes G2, where G1 acts on qubit 1 only and G2 acts on qubit 2 only.
  26. D

    Reading the value of a qubit without changing its value

    From the http://physicsworld.com/cws/article/news/23637 How can that be possible? Isn't that a violation of the No-cloning theorem?
  27. L

    Which operator is suitable to define a qubit?

    What requirements must an observable A meet to be usefull as a qubit for quantum computers? I think that the wave function must have time independent coefficients in the base of A (when we are not applying quantum gates). This means that expected value <A> must be constant, so the...
  28. D

    How Are the Coefficients of a Qubit's Density Matrix Constrained?

    What is the arbitrary density matrix of a mixed state qubit?
  29. B

    Pure Qubit Question: Does Alice Fulfill Bob's Demand?

    Hi, One can describe a pure qubit in two ways (onto the bloch-sphere): 1.) one take a (\alpha,\beta) , where \alpha,\beta are complex numbers and \left|\alpha\right|^{2}+\left|\beta\right|^{2}=1. 2.) with a real 3-dimensional unit vector. Bob wants that Alice generate one million random...
  30. michael879

    Understand Decoherence in Quantum Computers: How Heat Affects Qubits

    ok I just read something that doesn't make much sense to me. It said that quantum computers can only use reversible logic gates because irreversible gates generate heat/lost information. It makes sense to me that everything in physics is reversible and that NAND gates produce heat because...
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